Eddington-Malmquist bias in a cosmological context

In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars "in space" or gathered "from the sky". Malmquist (1920) derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work. We derived the Malmquist relation within a general cosmological framework, including Friedmann's model, analogously to the way Malmquist showed in 1936 that his formula is also valid in the presence of extinction in Euclidean space. We also discuss some conceptual aspects that explain the wide scope of the bias relation. The Malmquist formula for the intrinsic difference _m - M_0 = - sigma_M^2 dlna(m)/dm is also valid for observations made in an expanding Friedmann universe. This is holds true for bolometric and finite-band magnitudes when a(m) refers to the distribution of observed (uncorrected for K-effect or z-dependent extinction) apparent magnitudes.Comment: 5 pages, 3 figures, A&A (in press

Revisiting the optical depth of spiral galaxies using the Tully-Fisher B relation

Aims. We attempt to determine the optical depth of spiral galaxy disks by a statistical study of new Tully-Fisher data from the ongoing KLUN+ survey, and to clarify the difference between the true and apparent behavior of optical depth. Methods. By utilizing so-called normalized distances, a subsample of the data is identified to be as free from selection effects as possible. For these galaxies, a set of apparent quantities are calculated for face-on positions using the Tully-Fisher diameter and magnitude relations. These values are compared with direct observations to determine the mean value of the parameter C describing the optical depth. Results. The present study suggests that spiral galaxy disks are relatively optically thin tauB = 0.1, at least in the outermost regions, while they appear in general to be optically thick tauB > 1 when the apparent magnitude and average surface brightness are studied statistically.Comment: 9 pages, 13 figures, accepted for publication in Astronomy & Astrophysic

Kinematics of the local universe IX. The Perseus-Pisces supercluster and the Tolman-Bondi model

We study the mass distribution and the infall pattern of the Perseus-Pisces (PP) supercluster. First we calculate the mass of the central part of PP, a sphere with a radius of 15/h Mpc centered at (l,b)=(140.2\deg ,-22.0\deg), d=50/h Mpc, using the virial and other estimators. We get M_{PP} = 4 -- 7 /h 10^{15} M_{sun}, giving mass-to-light ratio 200 -- 600 h M_{sun} / L_{sun}, and overdensity \delta \approx 4. The radially averaged smoothed density distribution around the PP is inputted to the Tolman-Bondi (TB) equations, calculated for different cosmologies: \Omega_0 = [0.1,1], \Omega_{\Lambda} = 1-\Omega_0 or 0. As a result we get the infall velocities towards the PP center. Comparing the TB results to the peculiar velocities measured for the Kinematics of the Local Universe (KLUN) Tully-Fisher data set we get the best fit for the conditions \Omega_0 = 0.2 -- 0.4 and v_{inf} < 100 km/s for the Local Group infall towards the center of PP. The applicability of the TB method in a complex environment, such as PP, is tested on an N-body simulation.Comment: in press (A&A

Two-fluid matter-quintessence FLRW models: energy transfer and the equation of state of the universe

Recent observations support the view that the universe is described by a FLRW model with $\Omega_m^0 \approx 0.3$, $\Omega_{\Lambda}^0 \approx 0.7$, and $w \leq -1/3$ at the present epoch. There are several theoretical suggestions for the cosmological $\Lambda$ component and for the particular form of the energy transfer between this dark energy and matter. This gives a strong motive for a systematic study of general properties of two-fluid FLRW models. We consider a combination of one perfect fluid, which is quintessence with negative pressure ($p_Q = w\epsilon_Q$), and another perfect fluid, which is a mixture of radiation and/or matter components with positive pressure ($p = \beta \epsilon_m$), which define the associated one-fluid model ($p = \gamma \epsilon$). We introduce a useful classification which contains 4 classes of models defined by the presence or absence of energy transfer and by the stationarity ($w = const.$ and $\beta = const.$) or/and non stationarity ($w$ or $\beta$ time dependent) of the equations of state. It is shown that, for given $w$ and $\beta$, the energy transfer defines $\gamma$ and, therefore, the total gravitating mass and dynamics of the model. We study important examples of two-fluid FLRW models within the new classification. The behaviour of the energy content, gravitating mass, pressure, and the energy transfer are given as functions of the scale factor. We point out three characteristic scales, $a_E$, $a_{\cal P}$ and $a_{\cal M}$, which separate periods of time in which quintessence energy, pressure and gravitating mass dominate. Each sequence of the scales defines one of 6 evolution types

Dark energy domination in the Virgocentric flow

The standard \LambdaCDM cosmological model implies that all celestial bodies are embedded in a perfectly uniform dark energy background, represented by Einstein's cosmological constant, and experience its repulsive antigravity action. Can dark energy have strong dynamical effects on small cosmic scales as well as globally? Continuing our efforts to clarify this question, we focus now on the Virgo Cluster and the flow of expansion around it. We interpret the Hubble diagram, from a new database of velocities and distances of galaxies in the cluster and its environment, using a nonlinear analytical model which incorporates the antigravity force in terms of Newtonian mechanics. The key parameter is the zero-gravity radius, the distance at which gravity and antigravity are in balance. Our conclusions are: 1. The interplay between the gravity of the cluster and the antigravity of the dark energy background determines the kinematical structure of the system and controls its evolution. 2. The gravity dominates the quasi-stationary bound cluster, while the antigravity controls the Virgocentric flow, bringing order and regularity to the flow, which reaches linearity and the global Hubble rate at distances \ga 15 Mpc. 3. The cluster and the flow form a system similar to the Local Group and its outflow. In the velocity-distance diagram, the cluster-flow structure reproduces the group-flow structure with a scaling factor of about 10; the zero-gravity radius for the cluster system is also 10 times larger. The phase and dynamical similarity of the systems on the scales of 1-30 Mpc suggests that a two-component pattern may be universal for groups and clusters: a quasi-stationary bound central component and an expanding outflow around it, due to the nonlinear gravity-antigravity interplay with the dark energy dominating in the flow component.Comment: 7 pages, 2 figures, Astronomy and Astrophysics (accepted